A three$-$phase, $5hp,208V,60Hz$ induction motor runs at $1746$ rpm when it delivers rated output power. Determine:

a$)$ The number of poles of the machine.

b$)$ The slip at full load.

c$)$ The frequency of the rotor current.

d$)$ The speed of the rotor field with respect to the:

Stator,

Stator rotating field.

$.$ A three$-$phase, $460V,60Hz$ induction machine produces $100$ hp at the shaft at $1746$ rpm $.$ Determine the efficiency of the motor if rotational losses are $3500$ W and stator copper losses are $3000$ W $.$

A $440V,60Hz,6-$pole, $3-$phase induction motor is taking $50$ kVA at $0\mathrm{.}8$ PF and is running at a slip of $0\mathrm{.}025.$ The stator copper losses are $0\mathrm{.}5$ kW and rotational losses are $2\mathrm{.}5$ kW $.$ Compute:

a$)$ The rotor copper losses.

b$)$ The shaft power in hp and the shaft torque.

c$)$ The efficiency.